Off-momentum DA of RCS 3D_BM

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Off-momentum DA of RCS3D_BM QFF CC
AP meeting / December 8, 2004
Alexander Molodozhentsev Etienne Forest KEK
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Tune diagram
RCS_3DBM
Structure resonances
-QX2Qy6 Sextupole
Chromatic tune_shift ? 0.08 (dp/p ? 0.01)
-Qx3Qy12 Octupole
-Qx4Qy18 Decapole
-Qx5Qy24
Bare tunes Qx 6.68 Qy 6.27
--- scanning regions
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MADXRCS Twiss parameters (dp0.0)
Wkin 181 MeV ? 0.54523
WHY? Because MADX uses time as the independent
parameter instead of path-length
MAX_Dx 10 m !!!
MADX_Chromaticity -15 !!!
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Off-momentum particle motion(lattice1)
RCS_3DBM
PTC tracking Use path instead of timeSAD,
MAD8
Observation point SFX Dx ???
?p/p 0.01
Dx (SFX) 5.5 m
PTC Chromaticity (x/y) -8
5.5 cm
-15cm
15 cm
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Chromaticity definition
Sextupole field component
Path_length in ring
If the code uses the time instead of the path,
the chromaticity will be different in the case of
the low kinetic energy ds (c?) dt
Wkin 181 MeV ? 0.54523
then ?PATH 0.545 ?TIME !!!
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Dispersion function definition
Periodic dispersion function can be written
as Mario Conte, p.85
also depends on choice path or time
MAD dispersion (path) is about two time
bigger than SAD dispersion for Wkin181 MeV
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Off-momentum particle motion(lattice1)
PTC tracking Use time instead of path MADX
Observation point SFX Dx 10 m
?p/p 0.01
TDR Bore radius of SFX is (330/2) mm165 mm
SFX ?x 13m, ?y 6m ?xcenter-gtchamber
16.5-10.06.5 cm ?x,MAX ?(?x)2 / ?x
(6.5e-2)2/13 325 ?.mm.mrad Momentum
Acceptance for ?p/p 0.01
?x?p/p 10 cm
-15cm
15 cm
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Effects of the quadrupole fringe field
RCS_3DBM
ON-momentum particles
(1) Octupole-like effect at the leading
order excitation of the normal octupole
resonances
OFF-momentum particles
(2) De-tuning effect for the off-momentum
particles the end-field of the quadrupole
magnet gives the beam two kicks in the opposite
directions, which cancel for the paraxial
trajectories, but which gives a net focusing to
trajectories passing though at an angle. It
means that the fringe field of the quadrupole
magnets, which are located in the non- zero
dispersion sections, will provide the de-tuning
of the off-momentum particles. This effect
depends on the particle momentum and the
betatron amplitude, the dispersion and the slope
of the dispersion at the location of the
quadrupole magnet.
(3) Sextupole feeding-down component for
the off-momentum particles the pseudo-octupole
nonlinearity of the quadrupole magnet will be
feeding-down due to the closed orbit
displacement in the quadrupole magnets in the
non-zero dispersion regions (in the ARCs).
In this case the quadrupole fringe field can
contribute additional excitation to the
normal sextupole resonances.
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Tune variation for off-momentum particles
RCS_3DBM
Linear chromaticity (-8)
Without sextupole magnets for the chromaticity
correction
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Off-momentum DA (3D_BM)
RCS_3DBM
3D_BM Plus QFFHE
NO Sextupole CC
Observation point BM1 entrance (47)
dp/p0
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Off-momentum DA (3D_BM)
RCS_3DBM
3D_BM Plus QFFHE
Resonance -1,2 driving terms
NO Sextupole CC
Observation point BM1 entrance (47)
Resonance -1,2 driving terms for this case is 3
times smaller than for the corresponding tunes of
the on-momentum particles
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RCS_3DBM
Off-momentum DA (3D_BM)
3D_BM Plus QFFHE
NO Sextupole CC
Observation point BM1 entrance (47)
Increasing the resonance 4Qx27 for the
off-momentum particles by the feeding-down the
high-order field components of the 3D_BM
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Effect of the quadrupole fringe field for the
off-momentum particles
RCS_3DBM
3D_BM Plus QFFHE
NO Sextupole CC

• Contribution to the normal
• sextupole resonance by
• the sextupole feeding-down
• of the QFF pseudo-octupole
• some compensation effect

(1)
(2)
(2) Increasing of the normal octupole
resonance
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Off-momentum DA (3D_BM)
RCS_3DBM
3D_BM Plus QFFHE
NO Sextupole CC
Observation point BM1 entrance (47)
Main limitation of the off-momentum DA is caused
by the normal octupole resonance.
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Off-momentum DA (3D_BM)dp/p? 0.005
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Off-momentum DA (3D_BM)dp/p? 0.01
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synchrotron oscillation
Some speculation look at summary012-file
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On-momentum particle motion
RCS_3DBM
NO CC Sextupoles
Tune-scanning in the Qy direction
QX fix QY - vary
Main limitation of the on-momentum DA is caused
by the normal sextupole resonance
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Off-momentum (3D_BM) plus chromatic sextupole
magnets
RCS_3DBM
Changing of the tune for different (dp/p) before
(1) and after (2) the chromaticity correction
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Off-momentum DA after chromatic correction
RCS_3DBM
3D_BM Plus QFFHE
Sextupole CC
Observation point BM1 entrance (47)
Twiss Parameters (ßx)1/2 2.7848 m1/2, ?x
0.2517 (ßy)1/2 3.9030 m1/2, ?y 0.1990
(XY)MIN 2.75 cm
Ax (Xmax)2?x 190 ? mm mrad
Ay (Ymax)2?y 150 ? mm mrad
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On-momentum DA after chromatic correction
RCS_3DBM
result was presented October 27, 2004.
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To DO
RCS_3DBM

• correction of the normal sextupole resonance
• off-momentum particle motion after the
  correction

Presented for the AP-group December 8, 2004